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HELP deriving this equation?!?
I am studying physics and I don't know how the hell they derived s=vit + (1/2)at^2 (distance= initial velocity x time + 1/2 x acceleration x time squared) from the equations s=vt (distance = average velocity x time) and v=1/2at (distance= one half x acceleration x time).
I tried 3 times to make sense of it but every time I derive it I just end up with s= (vit + at^2)/2 (distance= one half x initial velocity x time + one half x acceleration x time squared)
DEAR GOD SOMEONE HELP THIS IS AN EMERGENCY IM DYING.
1 Answer
- ?Lv 59 years ago
Vav = average velocity
vi = initial velocity
vf = final velocity
a = Δv / Δt = (vf - vi) / (t - 0) = (vf - vi) / t
a = (vf - vi) / t
vf = vi + at ........... eq. 1
s = Vav * t ........... eq. 2
Vav = 1/2(vi + vf) ... eq. 3
Substitute eq. 3 into eq. 2
s = Vav * t
s = 1/2(vi + vf) * t
Substitute in vf from eq. 1
s = 1/2(vi + vi + at) * t
s = 1/2(2vi + at) * t ....... distribute the 1/2
s = (vi + 1/2at) * t
s = vit + 1/2at^2 ........... distribute the t
Not sure where that v = 1/2at came from...it's not correct.